A viable method for goodness-of-fit test in maximum likelihood fit

A test statistic is proposed to perform the goodness-of-fit test in the unbinned maximum likelihood fit. Without using a detailed expression of the efficiency function, the test statistic is found to be strongly correlated with the maximum likelihood function if the efficiency function varies smoothly. We point out that the correlation coefficient can be estimated by the Monte Carlo technique. With the established method, two examples are given to illustrate the performance of the test statistic.     

一种基于单似然检验的高光谱图像小目标检测器

针对背景和目标的先验光谱特征未知的条件,给出一种基于单似然检验的高光谱图像小目标检测器。小目标相对于背景的低概率性使得高光谱图像数据对目标光谱信号的矩特征几乎不施加约束,可在最大熵条件下将广义似然比检验简化为对背景似然的单似然检验;利用全部数据样本建立无参估计模型以充分利用样本信息,从而得到基于单似然检验的高光谱图像小目标检测器。该检测器避免了统计模型误差和不明确物理含义特征对实际高光谱图像数据检测带来的影响。使用可见光/近红外波段机载I型实用型模块化成像光谱仪(OMIS-I)高光谱图像进行了实验,实验结果及相应理论分析表明该算法可有效检测高光谱图像中的空间低概率目标。     

The Anderson-Darling test of fit for the power-law distribution from left-censored samples

Maximum likelihood estimation and a test of fit based on the Anderson-Darling statistic are presented for the case of the power-law distribution when the parameters are estimated from a left-censored sample. Expressions for the maximum likelihood estimators and tables of asymptotic percentage points for the A² statistic are given. The technique is illustrated for data from the Dow Jones Industrial Average index, an example of high theoretical and practical importance in Econophysics, Finance, Physics, Biology and, in general, in other related sciences such as Complexity Sciences.     

Power law distribution in high frequency financial data? An econometric analysis

Power law distributions are very common in natural sciences. We analyze high frequency financial data from XETRA and the NYSE using maximum likelihood estimation and the Kolmogorov–Smirnov statistic to test whether the power law hypothesis holds also for these data. We find that the universality and scale invariance properties of the power law are violated. Furthermore, the returns of Daimler Chrysler and SAP traded simultaneously on both exchanges follow a power law at one exchange, but not at the other. These results raise some questions about the no-arbitrage condition. Finally, we find that an exponential function provides a better fit for the tails of the sample distributions than a power law function.     

Simultaneous Inference for High-Dimensional Approximate Factor Model

This paper studies simultaneous inference for factor loadings in the approximate factor model. We propose a test statistic based on the maximum discrepancy measure. Taking advantage of the fact that the test statistic can be approximated by the sum of the independent random variables, we develop a multiplier bootstrap procedure to calculate the critical value, and demonstrate the asymptotic size and power of the test. Finally, we apply our result to multiple testing problems by controlling the family-wise error rate (FWER). The conclusions are confirmed by simulations and real data analysis.     

Combined estimation for multi-measurements of branching ratio

A maximum likelihood method is used to deal with the combined estimation of multi-measurements of a branching ratio, where each result can be presented as an upper limit. The joint likelihood function is constructed using observed spectra of all measurements and the combined estimate of the branching ratio is obtained by maximizing the joint likelihood function. The Bayesian credible interval or upper limit of the combined branching ratio,is given in cases both with and without inclusion of systematic error.     

基于Stiefel流形的粒子滤波器研究

为了解决粒子滤波的粒子退化和粒子多样性丧失问题,提出了一种基于Stiefel流形的粒子滤波算法.该算法将系统模型置于Stiefel流形上,用朗之万分布描述过程转移概率分布,用矩阵正态分布表示似然函数分布,在流形分布上进行粒子采样.在计算加权粒子的均值时,将流形嵌入到欧氏空间中,先计算欧氏空间中的粒子均值,再将计算结果投影到嵌套流形上,这就排除了噪声统计特性对粒子权重方差的影响,得到了一种受系统状态模型限制较少的重要性概率密度函数通用选择方案.仿真时选取单变量非静态增长模型,仿真结果验证了该算法的实时性、鲁棒性,滤波精度和滤波效率均比无味粒子滤波算法更好.     

Detection of gravitational waves using a network of detectors

We formulate the data analysis problem for the detection of the Newtonian coalescing-binary signal by a network of laser interferometric gravitational wave detectors that have arbitrary orientations, but are located at the same site. We use the maximum likelihood method for optimizing the detection problem. We show that for networks comprising of up to three detectors, the optimal statistic is just the matched network-filter. Alternatively, it is simply a linear combination of the signal-to-noise ratios of the individual detectors. This statistic, therefore, can be interpreted as the signal-to-noise ratio of the network. The overall sensitivity of the network is shown to increase roughly as the square-root of the number of detectors in the network. We further show that these results continue to hold even for the restricted post-Newtonian filters. Finally, our formalism is general enough to be extended, in a straightforward way, to address the problem of detection of such waves from other sources by some other types of detectors, eg., bars or spheres, or even by networks of spatially well-separated detectors.     

铷原子D1线真空压缩光场的产生及态重构

碱金属原子是光量子存储的良好介质,与碱金属原子共振的非经典光场是量子信息处理的重要资源.本文采用周期极化磷酸氧钛晶体作为非线性介质,利用参量振荡过程产生了795 nm(铷原子D1线)的真空压缩光场.通过对平衡零拍探测系统的时域信号进行采集,得到压缩光场不同相位角下的噪声分布;利用极大似然估计法对压缩光场进行了态重构,得到了密度矩阵及相空间的Wigner函数.理论计算了真空压缩场的光子数分布和Wigner函数,并对理论计算结果和极大似然重构结果进行了分析和比较.     

Assessing symmetry of financial returns series

Testing symmetry of a probability distribution is a common question arising from applications in several fields. Particularly, in the study of observables used in the analysis of stock market index variations, the question of symmetry has not been fully investigated by means of statistical procedures. In this work a distribution-free test statistic T_n for testing symmetry, derived by Einmahl and McKeague, based on the empirical likelihood approach, is used to address the study of symmetry of financial returns. The asymptotic points of the test statistic T_n are also calculated and a procedure for assessing symmetry for the analysis of the returns of stock market indices is presented.     

基于机器视觉的最大似然位姿估计算法

针对现有位姿估计算法对采样数据不做任何的统计假设,缺少评判标准等问题,从信号的概率密度函数出发,推导了基于机器视觉的最大似然位姿估计的一般形式,并证明利用单幅图像时,在各向同性高斯噪声情况下传统迭代算法与最大似然估计等效。推导了位姿估计的克拉美-罗界,给出了位姿估计的方差下限。根据仿真结果可以看出,利用10张图像时,最大似然算法在噪声功率大于5dB的情况下,性能明显优于传统迭代算法,证明适当增加图像数可有效提高估计性能。     

基于时间反演电磁波的稀疏阵列单频信号空间功率合成

基于时间反演技术, 建立了稀疏阵列单频信号相干合成的数学模型, 定义了合成效率函数概念, 推导出合成信号幅度最大时刻目标点合成效率值的统计特征与相位误差及阵元数的关系表达式, 并通过理论分析与仿真计算研究了相位误差对时间反演单频信号合成效果的影响. 分析表明, 当其他参数确定时, 假设相位误差服从一定范围的均匀分布, 且相互独立, 则峰值功率时刻的合成效率均值与阵元数无关, 仅与误差分布范围有关; 峰值功率时刻的合成效率方差与两者均相关, 且误差分布范围确定时, 阵元数越大, 峰值功率时刻的合成效率方差越小. 仿真计算结果表明, 即使存在一定的相位误差, 利用时间反演技术, 仍可实现单频信号在目标点邻域的相干合成及能量聚焦; 对相位误差的控制精度应结合需求与实现条件折中考虑. 本文的方法与结论可为研究稀疏阵列功率合成在高功率微波武器等技术中的应用提供理论依据.     

Determination of Threshold Values of the Generalized Likelihood Ratio in the Problem of Detecting Partially Coherent Spatial Signals in the Case of Short Samples

In this paper, we solve the problem of detecting multidimensional Gaussian complex signals with an a priori unknown spatial covariance matrix against the background of spatially nonuniform Gaussian noise with unknown power in the case of a fixed false-alarm probability. For an arbitrary sample size, exact analytical expressions are obtained for the moments of a decision statistic represented in the form of a generalized likelihood ratio raised to power reciprocal of a positive integer. The series expansion of the probability density function of the decision statistic in terms of orthogonal Jacobi polynomials is obtained by the method of moments. We use numerical simulation to demonstrate the high accuracy of approximating the probability density and finding the threshold value of the decision statistic. The obtained results hold for the case of short samples whose sizes are comparable with the number of elements of a receiving antenna.     

Cross-Polarized Single Photon Emission from Single Semiconductor Quantum Dots with V-Type Level Driven by Pulse Field

The statistic properties of photon emissions from single semiconductor quantum dots with V-type level driven by pulses are investigated theoretically. Based on quantum regression theorem and master equations, the dynamic equations of the second-order correlation function of the photon emissions are deduced. The calculated results reveal that the efficiency of single photon emissions from two orthogonal polarization eigenstates |x〉and |y〉) reaches the maximum when the input pulses area is about π, and the probability of the cross-polarized single photon emission from |x 〉 and |y 〉decreases with increasing of pulse width.     

Maximum likelihood subband polynomial regression for robust speech recognition

In this paper, we propose a model adaptation algorithm based on maximum likelihood subband polynomial regression (MLSPR) for robust speech recognition. In this algorithm, the cepstral mean vectors of prior trained hidden Markov models (HMMs) are converted to the log-spectral domain by the inverse discrete cosine transform (DCT) and each log-spectral mean vector is divided into several subband vectors. The relationship between the training and testing subband vectors is approximated by a polynomial function. The polynomial coefficients are estimated from adaptation data using the expectation–maximization (EM) algorithm under the maximum likelihood (ML) criterion. The experimental results show that the proposed MLSPR algorithm is superior to both the maximum likelihood linear regression (MLLR) adaptation and maximum likelihood subband weighting (MLSW) approach. In the MLSPR adaptation, only a very small amount of adaptation data is required and therefore it is more useful for fast model adaptation.     

Modal identification based on Gaussian continuous time autoregressive moving average model

A new time-domain modal identification method of the linear time-invariant system driven by the non-stationary Gaussian random force is presented in this paper. The proposed technique is based on the multivariate continuous time autoregressive moving average (CARMA) model. This method can identify physical parameters of a system from the response-only data. To do this, we first transform the structural dynamic equation into the CARMA model, and subsequently rewrite it in the state-space form. Second, we present the exact maximum likelihood estimators of parameters of the continuous time autoregressive (CAR) model by virtue of the Girsanov theorem, under the assumption that the uniformly modulated function is approximately equal to a constant matrix over a very short period of time. Then, based on the relation between the CAR model and the CARMA model, we present the exact maximum likelihood estimators of parameters of the CARMA model. Finally, the modal parameters are identified by the eigenvalue analysis method. Numerical results show that the method we introduced here not only has high precision and robustness, but also has very high computing efficiency. Therefore, it is suitable for real-time modal identification.     

基于最大似然的单通道交叠激光微多普勒信号参数分离估计

利用激光对目标微弱振动进行探测有利于获得明显的微多普勒效应,这为精确估计目标微动特征参数,实现对目标的分类和精细识别提供了可能.但对于多散射点或多目标激光探测,信号为单通道多分量微动混合的形式,而且补偿目标主体运动后,数值上相近的微动参数还会导致信号在时频域存在严重的交叠.为从这类混合信号中精确估计各分量的微动参数,本文提出了基于最大似然框架的参数分离估计方法.利用精细化扫描的奇异值比谱法从混合信号中获得目标微动频率,并得到各分量的幅值比信息.推导了微动参数最大似然估计的解析表达形式,根据激光微多普勒信号的特点从频谱能量分布的角度重新设计了似然函数,解决了传统似然函数在激光微动信号中出现的高度非线性问题,降低了初始化的要求,提高了抗噪性能,并采用马尔可夫-蒙特卡罗方法具体实现了参数的估计.在微动参数得到估计的基础上给出了信号的幅值和初相的估计方法.用本文方法对仿真和实验数据进行处理,得到了接近克拉美罗下界的估计结果,验证了方法的有效性.与传统非参数化估计方法的对比结果体现了所提方法对混合微动参数精确估计上的优势.     

Maximum likelihood estimator of operational modal analysis for linear time-varying structures in time–frequency domain

This paper investigates the problem of modal parameter estimation of time-varying structures under unknown excitation. A time–frequency-domain maximum likelihood estimator of modal parameters for linear time-varying structures is presented by adapting the frequency-domain maximum likelihood estimator to the time–frequency domain. The proposed estimator is parametric, that is, the linear time-varying structures are represented by a time-dependent common-denominator model. To adapt the existing frequency-domain estimator for time-invariant structures to the time–frequency methods for time-varying cases, an orthogonal polynomial and z-domain mapping hybrid basis function is presented, which has the advantageous numerical condition and with which it is convenient to calculate the modal parameters. A series of numerical examples have evaluated and illustrated the performance of the proposed maximum likelihood estimator, and a group of laboratory experiments has further validated the proposed estimator.     

City size distributions for India and China

This paper studies the size distributions of urban agglomerations for India and China. We have estimated the scaling exponent for Zipf’s law with the Indian census data for the years of 1981-2001 and the Chinese census data for 1990 and 2000. Along with the biased linear fit estimate, the maximum likelihood estimate for the Pareto and Tsallis q-exponential distribution has been computed. For India, the scaling exponent is in the range of [1.88, 2.06] and for China, it is in the interval [1.82, 2.29]. The goodness-of-fit tests of the estimated distributions are performed using the Kolmogorov-Smirnov statistic.     

Information Measure in Terms of the Hazard Function and Its Estimate

It is well-known that some information measures, including Fisher information and entropy, can be represented in terms of the hazard function. In this paper, we provide the representations of more information measures, including quantal Fisher information and quantal Kullback-leibler information, in terms of the hazard function and reverse hazard function. We provide some estimators of the quantal KL information, which include the Anderson-Darling test statistic, and compare their performances.